Study of new physics effects in $\bar B_s\to D^{(*)}_s\tau^-\bar\nu_\tau$ semileptonic decays using Standard Model lattice QCD form factors and heavy quark effective theory

We benefit from the lattice QCD determination of the Standard Model (SM) form factors for the $\bar B_s\to D_s^{*}$ and $\bar B_s\to D_s$ semileptonic decays carried out by the HPQCD collaboration in Refs. Phys. Rev. D 105, 094506 (2022) and Phys. Rev. D 101, 074513 (2020), and the heavy quark effective theory (HQET) relations for the analogous $B\to D^{(*)}$ decays obtained by F.U. Bernlochner et al. in Phys. Rev. D 95, 115008 (2017), to extract the leading and sub-leading Isgur-Wise functions for the $\bar B_s\to D_s^{(*)}$ decays. Further use of the HQET relations allows us to evaluate the corresponding scalar, pseudoscalar and tensor form factors needed for a phenomenological study of new physics (NP) effects on the $\bar B_s\to D_s^{(*)}$ semileptonic decay. At present, the experimental values for the ratios ${\cal R}_{D^{(*)}}=\Gamma[\bar B\to D^{(*)}\tau^-\bar\nu_\tau]/\Gamma[\bar B\to D^{(*)}e^-(\mu^-)\bar\nu_{e(\mu)}]$ are the best signal in favor of lepton flavor universality violation (LFUV) seen in charged current (CC) $b\to c$ decays. In this work we conduct a study of NP effects on the $\bar B_s\to D_s^{(*)}\tau^- \bar\nu_\tau$ semileptonic decays by comparing tau spin, angular and spin-angular asymmetry distributions obtained within the SM and three different NP scenarios. As expected from SU(3) light-flavor symmetry, we get results close to the ones found in a similar analysis of the $\bar B\to D^{(*)}$ case. The measurement of the $\bar B_s\to D_s^{(*)}\ell\bar\nu_\ell$ semileptonic decays, which is within reach of present experiments, could then be of relevance in helping to establish or rule out LFUV in CC $b\to c$ transitions.